1. Engineering 1
Structural
Analysis
Tom Rebold

2. To design a bridge, the internal forces must be understood

3. Outline Force vectors Adding vectors Tension and Compression
Assumptions
Method of Joints

4. Vectors help us understand forces
Have a direction
And a size
Applied to bridges

5. Adding Vectors Imagine you walk N for 2 blocks,
turn and walk E for 2 blocks
turn and walk S for 2 blocks
Where did you end up?
That’s exactly how you add vectors
For a bridge not to collapse, all the forces at each joint must add to zero
i.e. you arrive back where you started

6. Tension and Compression
Who knows the difference?
In our diagrams, a force acting toward the center of a member (pulling on a pin) is tension. A force pushing a pin outward from a member is compression

7. Assumptions All loadings are applied to the joints
The members are joined by smooth pins
Conclusion 1: each truss member acts as a two force member
Conclusion 2: forces can only elongate (tension) or shorten (compress) a member
Also assume the weight of the members is small compared to the load
At each joint, the sum of all forces must be zero (or the bridge would collapse)

8. Method of Joints
Start at a joint with one known force and at most two unknown forces
Draw the “free-body” diagram of a joint, removed from it’s surroundings
Apply the known force to the joint, then zero out the known force by adjusting the force vectors along the other two members
Once you determine the force at one end of a member, it’s the same force at the other end
Continue to analyze each joint, where at most you have two unknown forces to solve

9. We now demonstrate on the homework examples
1 end is anchored to the ground
1 end is set on a roller

10. Problem 2

11. Computer Analysis Tool at http://www.jhu.edu/virtlab/bridge/bridge.htm

12. As the length increases, so do the forces…

13. Shifting the load…